Yes, difference just is that contraceptive pills are only given if you go ask them yourself, with vaccination is bit different if there is will to have good coverage, majority have to take it and people might feel forced to have it if it's needed for travelling or other things.
Covid either is not killing too many young people, if you are 18-30, your chance to die for covid or even getting very severe one is quite small as well based on available data (of course there are loads of stories where some healthy young person got it really bad but that goes with most of this kind of deceases, (i think i recovered some months from pneumonia when i was bit over 20, it wasn't fun when couldn't do anything physical).
Of course we don't have enough accurate data about long covid or however it should be called, but early predictions about 10% of covid patients suffering about it is bit same than say that this vaccine is dangerous and cause loads of severe side effects. These long covid numbers are mainly done by asking from people themselves if you feel sick etc... without medical diagnose which might not be most accurate method, then one thing in these is that most common thing of long covid seems to be anxiety which kind of possibly is not directly caused by covid but whole experience of getting virus which all in telly tell will kill you, being uncertain from many things during these worldwide restrictions that do we ever get back to normal etc... for sure this situation have caused amount of anxiety for many people who haven't have covid but have been negatively affected by losing your job, your studies not going well, if not yourself, somebody close to you at least have been hit by covid or these restrictions etc.. By time we have more medical facts about long covid but currently it sounds bit far that 10% of covid patients suffer from it.
Unfortunately it feels sometimes that even scientist have lost bit of their ethics in this one and all studies and statements are not always made 100% "science first" attitude but more to backup their own opinions instead of getting real results to benefit all, even it would prove somebody been wrong in something which is quite questionable as scientists used to always be once who first change their opinion when there is new information available, now even some very well educated research people seem to give priority to their personal agenda prior true science, which is really sad and totally against their traditional ethics.